Phantom (formerly Fiji), my other betta who is posted in 'Show off' forum, is actually a 'monster' betta due to his size (he is massive). A 'monster' betta is along the same size as a Petco "king"-sized betta accept Phantom is a Half-moon instead of a Plakat which seems to be the only variety they ever have in larger sizes (and I don't care for as much).
'Giant' bettas by far are the largest betta and very rare (3-4 inches body alone!). I ordered one from Thailand years ago ($80 not including shipping and import fees). He was a "mustard gas" coloration (look at aquabid.com for similar colored combinations).
Andre had a blackish/silvery, dragon scaled body with a bright yellow tail. The yellow in his tail slowly faded as it fanned out from his body creating a cool dual-color effect. He had a dark, black-lace rim around the edge of his tail. Andre was a half-moon and gorgeous.
Unfortunately this was years ago and I don't have a photo of him. 'giants' do not tend to live as long as my other bettas did (I have only ever had one so it may not be fair to say that ALL 'giants' do not live as long). But I called him Andre (the giant) and he was super healthy his whole life and lived about 2 years.
But my understanding of 'sizes' are: Regular->Monster->Giant